AP EAMCET · PHYSICS · Magnetic Effects of Current

Torque required to hold a small circular coil of $10$ turns, $2 \times 10^{- 4} m^{2}$ area and carrying $0.5 A$ current is the middle of a long solenoid of $10^{3}$ turns per meter carrying $3 A$ current, with its axis perpendicular to the axis of the solenoid is

A $12 π \times 10^{- 7} N m$
B $6 π \times 10^{- 7} N m$
C $4 π \times 10^{- 7} N m$
D $2 π \times 10^{- 7} N m$

Verified Solution

Answer & Solution

Correct Answer

(A) $12 π \times 10^{- 7} N m$

Step-by-step Solution

Detailed explanation

Dipole moment of the coil, M=NAI=10×2×10-4×0.5 ⇒M=10-3 A m2 Magnetic field due to solenoid, B=μ0nI=4π×10-7×103×3 ⇒B=μ0nI=12π×10-4 T Torque =MBsinθ=12π×10-4×10-3 Torque…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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Torque required to hold a small circular coil of 10 turns, 2×10-4 m2 area and carrying 0.5 A current is the middle of a long solenoid of 103 turns per meter carrying 3 A current, with its axis perpendicular to the axis of the solenoid is

Step-by-step Solution

Torque required to hold a small circular coil of $10$ turns, $2 \times 10^{- 4} m^{2}$ area and carrying $0.5 A$ current is the middle of a long solenoid of $10^{3}$ turns per meter carrying $3 A$ current, with its axis perpendicular to the axis of the solenoid is